Soften the fennel in boiling water for about 30 minutes. Remove them from the water and let them cool. Sprinkle with coarse salt and dried mint, then drizzle with oil. Grill on a cast-iron pan or use an air fryer for 10 minutes.
Preheat the oven to 390°F (200°C).
Peel the beets and wrap them in aluminum foil. Place them in a baking dish and cover them halfway with water. Bake for 30 minutes, or until the beets are tender. If necessary, add water to the dish during baking.
Grind all the pesto ingredients in a food processor. Pour the pesto onto a large plate, then arrange the fennel and beets on top. Sprinkle with salt and drizzle with olive oil and lemon juice.